Step 1: Identify constants $ \color{blue}{ b }$ and $\color{red}{ c }$. ( $ \color{blue}{ b }$ is a number in front of the $ x $ term and $ \color{red}{ c } $ is a constant). In our case:
$$ \color{blue}{ b = 2 } ~ \text{ and } ~ \color{red}{ c = -15 }$$Now we must discover two numbers that sum up to $ \color{blue}{ 2 } $ and multiply to $ \color{red}{ -15 } $.
Step 2: Find out pairs of numbers with a product of $\color{red}{ c = -15 }$.
PRODUCT = -15 | |
-1 15 | 1 -15 |
-3 5 | 3 -5 |
Step 3: Find out which pair sums up to $\color{blue}{ b = 2 }$
PRODUCT = -15 and SUM = 2 | |
-1 15 | 1 -15 |
-3 5 | 3 -5 |
Step 4: Put -3 and 5 into placeholders to get factored form.
$$ \begin{aligned} x^{2}+2x-15 & = (x + \color{orangered}{\square} )(x + \color{orangered}{\square}) \\ x^{2}+2x-15 & = (x -3)(x + 5) \end{aligned} $$